Peter is really the word “petros” (stone) and rock is the word “petra” (massive rock) as written in the original greek scriptures, therefore, is is upon Christ Himself that the Church is built. (See other references: I Peter 2:4-8 and I Corinthias 3:11).

With all due respect I want to comment that what Heidi says is correct; in the greek text from Matthew 16:18 mentioned by Moritzchen, the word for Peter is petros (a small stone) and for rock it is petra (a foundation boulder). Peter himself explains that Christ is the Rock (see passage mentioned above by Heidi I Peter 2:4-8).

Regarding the translation, it is very common to use Rock to refer to the Piedra de la iglesia.